Consider a binomial experiment with n = 4 trials where the probability of success on a single trial is p = 0.25. (For each answer, enter a number. Round your answers to three decimal places.) (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

In binomial experiment with 4 trials, Probabilities shown below.

               and  

The Probability of r number of successes in n trials is given by a binomial expression,

Where p represent probability of success and q represent probability of unsuccessful.

Number of trials, n = 4

Probability of success, p = 0.25  and  q = 1 - 0.25 = 0.75

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(a) 0.32

(b) 0.68

Step-by-step explanation:

It is given that a binomial experiment is carried out.

n = 4 trials

Probability of success, p = 0.25

We know that in a binomial experiment:

Probability of success + Probability of failure = 1

p + q = 1

So, q = 1 - 0.25 = 0.75

Probability of 'r' number of successes in 'n' trials of a binomial experiment is given as:

(a) P(r = 0) = ?

Putting values of x = 0, p and q:

(b) Find P(r ≥ 1)  = ?

Using complement rule:

P(r =0 ) + P(r ≥ 1)  = 1

0.32 + P(r ≥ 1)  = 1

P(r ≥ 1)  = 1 - 0.32

P(r ≥ 1)  = 0.68

So, the answer are:

(a) 0.32

(b) 0.68